Answer:
Part 1) [tex]f(x)=4x+3[/tex]
Part 2) [tex]f(x)=2x+1[/tex]
Part 3) [tex]f(x)=x-4[/tex]
Step-by-step explanation:
Table 1
step 1
Find the slope
take two points from the data in the table
(0,3) and (3,15)
The formula to calculate the slope between two points is equal to
[tex]m=\frac{y2-y1}{x2-x1}[/tex]
substitute
[tex]m=\frac{15-3}{3-0}[/tex]
[tex]m=\frac{12}{3}=4[/tex]
step 2
Find the linear function in slope intercept form
[tex]f(x)=mx+b[/tex]
we have
[tex]m=4\\b=3[/tex]
substitute
[tex]f(x)=4x+3[/tex]
Table 2
step 1
Find the slope
take two points from the data in the table
(2,5) and (5,11)
The formula to calculate the slope between two points is equal to
[tex]m=\frac{y2-y1}{x2-x1}[/tex]
substitute
[tex]m=\frac{11-5}{5-2}[/tex]
[tex]m=\frac{6}{3}=2[/tex]
step 2
Find the linear function in slope intercept form
[tex]f(x)=mx+b[/tex]
we have
[tex]m=2\\point\ (2,5)[/tex]
Solve for b
substitute
[tex]5=2(2)+b\\b=5-4\\b=1[/tex]
therefore
[tex]f(x)=2x+1[/tex]
Table 3
step 1
Find the slope
take two points from the data in the table
(5,1) and (8,4)
The formula to calculate the slope between two points is equal to
[tex]m=\frac{y2-y1}{x2-x1}[/tex]
substitute
[tex]m=\frac{4-1}{8-5}[/tex]
[tex]m=\frac{3}{3}=1[/tex]
step 2
Find the linear function in slope intercept form
[tex]f(x)=mx+b[/tex]
we have
[tex]m=1\\point\ (5,1)[/tex]
Solve for b
substitute
[tex]1=1(5)+b\\b=1-5\\b=-4[/tex]
therefore
[tex]f(x)=x-4[/tex]
